Alloys consisting of Nickel and Titanium, show the so called shape memory effect, based on a diffusion-less, martensitic transformation. Compounds showing this effect have found applications, ranging from medical technology to space engineering. By alloying the system with Hafnium, the transition temperature of the martensitic transformation can be raised. In this work the transition behaviour of the system Nickel – Titanium – Hafnium within its high temperature phase is studied, using ab-initio methods. Goal is the calculation of the systems free energy with respect to temperature and composition of the alloy. Based on a cluster expansion method (CE), the groundstate formation energy of the alloy with respect to the systems configuration has been calculated. To study the temperature dependence of the system, Monte Carlo (MC) simulations based on the CE are performed. The applied MC code is part of the ATAT (Alloy Theoretic Automated Toolkit) toolkit. Convergence tests for the parameters of the MC simulations are performed. Using the converged parameters, MC simulations for the groundstate configurations at different temperatures are done. Using the thermodynamic data obtained from MC calculations, selected regions of the phase diagram for grondstate configurations are predicted.